OFFSET
0,2
COMMENTS
This net may be regarded as a tiling of the plane by 9-gons and triangles. There are two kinds of vertices: (a) 9^3 vertices, where three 9-gons meet, and (b) 3.9^2 vertices, where a triangle and two 9-gons meet. The present sequence is the coordination sequence with respect to a vertex of type 9^3. See also A319980.
LINKS
Muniru A Asiru, Table of n, a(n) for n = 0..300
Jean-Guillaume Eon, Geometrical relationships between nets mapped on isomorphic quotient graphs: examples, Journal of Solid State Chemistry 138.1 (1998): 55-65. See Fig. 1.
Jean-Guillaume Eon, Algebraic determination of generating functions for coordination sequences in crystal structures, Acta Cryst. A58 (2002), 47-53. See Section 8.
N. J. A. Sloane, A portion of the (9^3, 3.9^2) net
FORMULA
G.f.: (1+3*x+6*x^2+4*x^3+6*x^4+3*x^5+x^6)/(1-x^3)^2.
a(n) = (1/2)*(3*n + lcm(n,3)), for n>=1. - Ridouane Oudra, Jan 22 2021
MAPLE
seq(coeftayl((1+3*x+6*x^2+4*x^3+6*x^4+3*x^5+x^6)/(1-x^3)^2, x = 0, k), k=0..60); # Muniru A Asiru, Feb 13 2018
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 24 2001
STATUS
approved